Theorems · Theorem · commutative algebra
IsHausdorff.eq_iff_smodEq
∀ {R : Type u_1} [inst : CommRing R] {I : Ideal R} {M : Type u_4} [inst_1 : AddCommGroup M] [inst_2 : Module R M]
[IsHausdorff I M] {x y : M}, x = y ↔ ∀ (n : ℕ), x ≡ y [SMOD I ^ n • ⊤]- Defined in
- Mathlib.RingTheory.AdicCompletion.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- Top.topstatement and proof · cited by 9,680
- Submodulestatement · cited by 7,192
- Idealstatement and proof · cited by 4,748
- sub_zeroproof · cited by 938
- sub_eq_zeroproof · cited by 407
- SModEqstatement and proof · cited by 80
- IsHausdorffstatement and proof · cited by 37
- IsHausdorff.haus'proof · cited by 4
Cited by6
Results whose statement or proof uses this declaration.
- Perfection.teichmullerFun_spec'proof · cited by 3
- IsHausdorff.StrictMono.funextproof · cited by 1
- IsHausdorff.StrictMono.funext'proof · cited by 1
- IsHausdorff.funextproof · cited by 1
- IsHausdorff.funext'proof · cited by 1
- WittVector.fontaineTheta_teichmullerproof · cited by 0